Electrometry by Optical Charge Conversion of Defects in the Solid-State

ABSTRACT

Methods and systems are disclosed for sensing an environment electric field. In one exemplary implementation, a method includes disposing a sensor in the environment, wherein the sensor comprising a crystalline lattice and at least one optically-active defect in the crystalline lattice; pre-exciting the crystalline lattice to prepare at least one defect in a first charge state using a first optical beam at a first optical wavelength; converting at least one defect from the first charge state to a second charge state using a second optical beam at a second optical wavelength; monitoring a characteristics of photoluminescence emitted from the defect during or after the conversion of the at least one defect from the first charge state to the second charge state; and determining a characteristics of the electric field in the environment according to the monitored characteristics of the photoluminescence.

CROSS-REFERENCE

This application claims priority to the U.S. Provisional PatentApplication No. 62/630,503, filed on Feb. 14, 2018, and titled“Electrometry by Optical Charge Conversion of Defects in theSolid-State”, which is incorporated herein by reference in its entirety.

GOVERNMENT LICENSE RIGHTS

This invention was made with government support under grant numberW911NF-15-2-0058 awarded by the Army Research Laboratory, and grantnumber 1641099 awarded by the National Science Foundation. Thegovernment has certain rights in the invention.

BACKGROUND

Detection of electric charges and sensing of electric fields arecritical to applications including but not limited to metrology,electrical potential mapping, and characterization of electronic,optoelectronic or electromechanical devices. Traditional electrometrymay be based on, for example, direct sensing of electric forces,electro-optic Kerr effects, or using electron spin systems prepared andexcited by electromagnetic waves in the optical, radio-wave or microwavefrequency regime.

BRIEF DESCRIPTION OF THE DRAWINGS

The system and method may be better understood with reference to thefollowing drawings and description. Non-limiting and non-exhaustiveembodiments are described with reference to the following drawings. Thecomponents in the drawings are not necessarily to scale, emphasisinstead being placed upon illustrating the principles of the invention.

FIG. 1 illustrates an exemplary electrometry system for sensing anddetecting an environmental electric field.

FIG. 2 illustrates an exemplary sensor based on deep defects insemiconductors.

FIG. 3 illustrates an exemplary optical configuration for theelectrometry system of FIG. 1.

FIGS. 4a-4b illustrate transient photoluminescence measurements underthe optical configuration of FIG. 3.

FIG. 5 illustrates another exemplary optical configuration for theelectrometry system of FIG. 1.

FIG. 6 illustrates another exemplary optical configuration for theelectrometry system of FIG. 1.

FIG. 7 shows a logic flow for sensing an environmental electric fieldusing the electrometry system of FIG. 1.

FIG. 8 shows another logic flow for sensing an environmental electricfield using the electrometry system of FIG. 1.

FIG. 9 illustrates an exemplary electrometry system for sensing anddetecting an environmental electric field based on a heterodynedetection configuration.

FIG. 10 illustrates exemplary electrometry sensor configurations for usein heterodyne detection.

FIG. 11 illustrates exemplary heterodyne detection response at a beatfrequency.

FIG. 12 shows a logic flow for sensing an environmental electric fieldusing the electrometry system of FIG. 9.

FIGS. 13a-13d illustrate experimental configuration and measuredcharacteristics of an electrometry sensor based on deep defects in asemiconductor.

FIGS. 14a-14c show other measured characteristics of an electrometrysensor based on deep defects in a semiconductor.

FIGS. 15a-15b show further measured characteristics of an electrometrysensor based on deep defects in a semiconductor.

FIGS. 16a-16d show an exemplary application of the electrometry systemof FIG. 1 for measuring piezo electric field in a surface acoustic wavedevice.

FIGS. 17a and 17b show a comparison of exemplary measurement resultsbetween electrometry sensing configuration of FIG. 1 and heterodyneelectrometry sensing configuration of FIG. 9.

FIGS. 18a and 18b show comparison of exemplary heterodyne detectionresults between parallel and orthogonal reference electric field andelectric field being sensed.

FIGS. 19a-19d show exemplary coherent heterodyne detection results.

SUMMARY

This disclosure is directed to systems and methods for sensingenvironment electric fields using optical excitation and monitoring. Forexample, an electrometry sensor is used in the disclosed systems andmethods. The operation of the electrometry sensor is based on opticalcontrol of defect charge states in solid state host. The defect chargestates may be optically monitored by detecting their photoluminescence.The optical control of the defect charge state may be affected by thepresence of the environmental electric field. Such effect may bemonitored by analyzing the photoluminescence detected from the defectcharge states. As a result, characteristics of the environmentalelectric field may be determined.

In one implementation, a method for sensing an electric field in anenvironment is disclosed. The method includes pre-exciting a sensorcomprising a crystalline lattice and at least one defect in thecrystalline lattice to prepare the at least one defect in a first chargestate using a first optical beam at a first optical wavelength;converting the at least one detect from the first charge state to asecond charge state, using a second optical beam at a second opticalwavelength, wherein photoluminescence associated with the first chargestate being different from the second charge state; monitoring one ormore characteristics of a photoluminescence emitted during or after theconversion of the at least one defect from the first charge state to thesecond charge state; and determining one or more characteristics of theelectric field in the environment according to the one or more monitoredcharacteristics of the photoluminescence.

In another implementation, a system for sensing electric field isdisclosed. The system includes a sensor comprising a crystalline latticehaving at least one defect; a first optical source emitting a firstoptical beam at a first optical wavelength; a second optical sourceemitting a second optical beam at a second optical wavelength; anoptical detector for monitoring a photoluminescence from the sensor whenthe sensor is excited by the first optical beam and the second opticalbeam; a database; and a processor. The processor is configured toextract a first set of parameters from the photoluminescence; obtain asecond set of predetermined parameters from a referencephotoluminescence measured by the sensor and stored in the database;obtain a difference between the first set of parameters and the secondset of predetermined parameters; and determine an environmental electricfield of the sensor according to the difference.

In yet another implementation, another system for electrometry sensingis disclosed. The system includes a sensor comprising a crystallinelattice having at least one defect and a pair of electrodes for applyinga reference electric field; a first optical source emitting a firstoptical beam at a first optical wavelength; a second optical sourceemitting a second optical beam at a second optical wavelength; anoptical detector for generating a electric signal by collecting aphotoluminescence from the sensor when the sensor is excited by thefirst optical beam and the second optical beam in presence of theenvironmental electric field and the reference electric field; and acircuitry. The circuitry is configured to filter the first signal toobtain a signal component at a beat frequency between the environmentalelectric field and the reference electric field; and extract thecharacteristics of the environmental electric field based on the signalcomponent and characteristics of the reference electric field.

DETAILED DESCRIPTION

Embodiments of the invention and the various features and advantageousdetails thereof are explained more fully with reference to thenon-limiting embodiments that are illustrated in the accompanyingdrawings and detailed in the following description. Descriptions ofwell-known starting materials, processing techniques, measurementstechniques, components and equipment are omitted, so as not tounnecessarily obscure the embodiments of the invention in detail. Itshould be understood, however, that the detailed description and thespecific examples, while indicating preferred embodiments of theinvention, are given by way of illustration only and not by way oflimitation. Various substitutions, modifications, additions and/orrearrangements within the spirit and/or scope of the underlyinginventive concept will become apparent to one of ordinary skill in theart from this disclosure.

By way of introduction, the presence of electric charges or electricfields (herein referred generally as electric fields) in an environmentmay be determined and/or quantified. An electrometer may be used tomeasure such an electric field. Such an electrometer may include asensor that determines the electric field by, e.g., electricallymeasuring a resulting electromagnetic force or measuring otherparameters of the sensor as modified by the electric field, e.g.,electron spin state parameters affected by the electric field viaspin-electric coupling when the sensor includes electron spins. In someelectrometers, the sensor may be configured by an external excitation orstimulation (herein referred generally as excitation) into a particularstate before a measurement and determination of the environmentalelectric field can be performed. Such excitation may be introducedelectromagnetically via, e.g., a local radio-wave or microwave frequencyelectromagnetic wave for exciting electron spin states in anelectrometry sensor containing electron spins as the sensing elements.

In this disclosure, an electrometry sensor based on charge states ofdefects in solid-state materials, such as semiconductors, is disclosed.The sensor may be used to detect environmental electric field of a widefrequency range. The sensor may further be used to detect anenvironmental electric field exclusively using optical excitations andemitted photoluminescence. The optical excitation may be configured aseither pulsed excitation or continuous-wave (CW) excitation. Exclusivelyusing only optical excitation is advantageous because the optical beamsmay provide better penetration through substrates than radio-wave ormicrowave frequency electromagnetic waves (used, e.g., for electron spinexcitation in electron spin based sensors), and thus may facilitatedetecting local electric fields deep into a bulky sample. Further,all-optical excitation may avoid the requirement of including electrodeson the electrometry sensor for introducing external signals, e.g.radio-wave or microwave frequency electromagnetic wave excitationsources. Optical beams used for such excitation may be convenientlymanipulated in free space and/or guided in optical fibers. The opticalsignals produced by such a sensor may be guided and detected remotely,offering improved adaptability of such an electrometry sensor.

The electrometry sensor based on charge states of defects in solid-statematerials may be fabricated as an external/standalone/portable sensorthat may be placed into an environment for sensing the presence andstrength/frequency of electric fields. For example, the electrometrysensor may be placed in a scanning probe to measure fringe electricfield from an electronic device. The electrometry sensor may befabricated using diamond substrate for high-temperature tolerance andadapted to sense electric field in plasmas. It may be designed based onsilicon carbide and other bio-compatible materials and used inbio-sensing. The electrometry sensor may further be designed and used asinternal and embedded electric field sensing and monitoring elements inactive semiconductor devices. Its functioning in a semiconductor devicemay be monitored as indication of existence of defect states and be usedin material quality control in development of electronic devices. It maybe used for detecting electric field for characterization of highfrequency devices, such as Micro-Electro-Mechanical Systems (e.g.,microwave filter devices). For another example, such electrometry sensormay be adapted into acoustic wave devices (such as acoustic wavefilters) for their characterization. For different applications,suitable host materials and defects may be chosen.

FIG. 1 illustrates an exemplary electrometry system 100 for detecting anenvironmental electric field 101 (herein also referred to as theelectric field). The environmental electric field 101 may be, forexample, an electromagnetic wave of a particular frequency. In theimplementation of FIG. 1, the electrometry system 100 may include anelectrometry sensor (herein also referred as sensor) 102 disposed oralready present in an environment having the electric field 101, a firstoptical source 104, a second optical source 106, a photoluminescence(PL) excitation optical source 112, and a photodetector 118 fordetecting a PL 117 emitted from the sensor 102. While the implementationin FIG. 1 is illustrated in the context of using the electrometry sensor102 to measure external environmental electric filed, the sensor 102 maybe a built-in part of a host material or device and the systemillustrated in FIG. 1 may be used to measure internal electric fieldinside the host material and local to the built-in sensor. In addition,depending on the configuration and composition within the sensor 102(type of defects and defect states), a single source or two sourcesamong the first optical source 104, the second optical source 106, andthe PL excitation optical source may be included (for achieving, chargeconversion and PL excitation described below). For some otherimplementation of the sensor 102, more than three optical sources may beconfigured to achieve charge conversion and PL excitation.

The first optical source 104 and second optical source 106 may be arclamps, light emitting diodes or laser sources and may operate in eithera pulsed mode or a CW mode. The first optical source 104 and secondoptical source 106 may produce a first optical beam 109 and secondoptical beam 111. The optical beams 109 and 111 may further be processedby optics 108 and 110, respectively. Alternatively, optics 108 and 110may be a single group rather than separate groups of optical elements.Optical beams 109 and 111 may propagate in free space, optical fibers,or a combination of free space and optical fibers. The optics 108 and110 may include lenses, polarizers, and/or any other suitable free spaceor fiber optical elements.

The optical beams 109 and 111, after manipulation by the optics 108 and110, respectively, may be directed to the sensor 102. The first opticalbeam 109 may be used to prepare the sensor into a first charge state.The second optical beam 111 may perform optical pumping that convertsthe sensor from the first charge state to a second charge state. In oneimplementation, the first charge state is optically bright and thesecond charge state is optically dark. In other words, when the sensoris in the first charge state, a photoluminescence (PL) may be inducedwhereas when the sensor is in the second charge state, a PL may not beinduced. The preparation of the first charge state and the opticalconversion to the second charge state may be achieved using any otheroptical configurations. The PL 117 may be induced for the first chargestate by further excitation by the second optical beam 111.Alternatively, the PL for the first charge state may be induced using aseparate PL excitation optical beam 115 from a PL excitation opticalsource 112. The PL excitation optical source, for example, may be alaser source. The PL excitation optical beam 115 may be furtherprocessed by optics 114 before being directed to excite the sensor 102for inducing PL from the first charge state.

A charge conversion rate from the first charge state to the secondcharge state by the second optical beam 111 may be a function theenvironmental electric field 101. As such, the probability that thesensor remains in the optically bright first charge state may depend onthe environmental electric field 101 during or after the chargeconversion by the second optical beam 111. As a result, thecharacteristics of PL emission from the optically bright first chargestate depend on the environmental electric field 101. These PLcharacteristics may include but are not limited to, for example, theintensity of the PL emission and the transient dynamics of the PLemission. Such dependence may be used for detection and quantificationof the environmental electric field 101.

The first optical beam 109, the second optical beam 111, and the PLexcitation optical beam 115 may be adjusted respective to particularoptical wavelengths, λ₁, λ₂, and λ′, as illustrated in FIG. 1. In oneimplementation, the first optical beam 109 may be adjusted to awavelength λ₁, shorter than the wavelength λ₂ of the second optical beam111. The PL emission induced from the first charge state (bright state)may be at a particular wavelength λ₃. Wavelength λ₃ may be differentfrom λ₁, λ₂, and λ′. In one implementation, λ₃ may be longer than λ₂ ofthe second optical beam 111. In one implementation, the first opticalwavelength λ₁ may be in a wavelength range of 200 and 430 nanometers. Inanother implementation, the second optical wavelength λ₂ may be in awavelength range of 700 and 1100 nanometers.

As shown in FIG. 1, the PL 117 emitting from the sensor may becollected/guided by optics 116 and detected by the PL detector 118. ThePL detector 118, for example, may comprise a photo detector, such as aphotodiode, a photomultiplier tube, or other optical detectors. Thedetected electric signal by the PL detector 118 as a result of the PLemission 117 may be digitized and communicated to a processor 120 forfurther processing. The processor 120 may be in communication with adatabase 122. The database may contain reference PL characteristics ofreference PL from the sensor 102 pre-measured under presence of anyenvironmental electrical field. The processor 120 may be responsible fordetermining and quantifying the environmental electric field 101 basedon the measured PL characteristics from the sensor 102 under theinfluence of the environmental electric field 101 and the reference PLcharacteristics obtained from the database 122.

FIG. 2 shows an exemplary semiconductor structure 200 that may be usedas the electrometry sensor 102. In FIG. 2, the sensor 102 may include a3C, 4H or 6H silicon carbide lattices (3C—SiC, 4H—SiC, or 6H—SiC) 202.The silicon carbide lattices 202 may further include one or more defects204. The defects may be divacancies (VV) or silicon vacancies (V_(Si)).The vacancies may be produced by carbon implantation into the siliconcarbide lattices 202 followed by thermal annealing. The carbonimplantation, for example may be carried out in an exemplaryimplantation energy of 100 to 250 keV, resulting in a carbon dosage in arange of, for example, 10¹¹ and 10¹³ ion cm⁻². The thermal annealingfollowing the carbon implantation may be carried out at a temperature ina range of 600° C. and 1200° C. The thermal annealing may be performedfor various durations. For example, the carbon implanted silicon carbidelattices may be annealed for 1 hour, 2 hours, 3 hours, 4 hours, andother durations. The vacancies illustrated in the silicon carbidelattices of FIG. 2 may provide the optically bright first charge stateand the optically dark second charge state. The structure of FIG. 2 mayfurther provide charge conversion rate that depends on the presence,magnitude, orientation and/or frequency of the environmental electricfield. The term “defect” is used interchangeably with the term“impurity”.

Other material system providing similar charge states and chargeconversion characteristics may also be used as the electrometry sensor102. These exemplary material systems include but are not limited toLithium niobate (LiNbO3, having a bandgap ˜4 eV), quartz (having abandgap >6 eV), aluminum nitride (AlN, having a bandgap of ˜6 eV),gallium arsenide (GaAs, having a bandgap ˜1.4 eV), and diamond (having abandgap ˜5 eV).

FIG. 3 shows one exemplary timing configuration 300 of the first opticalbeam 109, the second optical beam 111, and the PL excitation opticalbeam 115. In the implementation of FIG. 3, the first optical beam 109 isconfigured in optical pulse 302 for preparing the sensor 102 into theoptically bright first charge state. Following the optical pulse 302 intime with a small delay Δ₁ 306, the second optical beam 111 isconfigured in optical pulse 304 for inducing a charge conversion betweenthe optically bright first charge state to the optically dark secondcharge state of the sensor 102. The amount of charge conversion by theoptical pulse 304 may depend on the environmental electric field 101.The delay Δ₁ 306 may be made as small as possible as long as there ispreferably insignificant time overlap between the optical pulse 302 andthe optical pulse 304 such that the sensor is sufficiently prepared intothe optically bright first charge state before the charge conversion bythe pulse 304 is initiated. In one implementation, the optical pulse 304may further induce PL emission from the sensor 102. In an alternativeimplementation, a separate PL excitation optical pulse 308 from the PLexcitation optical source (112 of FIG. 1) with wavelength λ′ may be usedfor inducing PL emission from the sensor 102. The PL excitation opticalpulse 308 may overlap with the optical pulse 304 in time or may beslight delayed 310 by, e.g., Δ₂.

FIGS. 4a and 4b illustrate measurements and analysis that may beperformed for detecting the environmental electric field 101 using theoptical configuration of FIG. 3 in conjunction with the systemconfiguration of FIG. 1. In particular, FIG. 4a illustrates a transientPL 404 from the sensor 102 following the pulse 304 (alternatively pulses304 and 308) as a function of time 402 following the PL excitation pulseby either the second optical beam (304 of FIG. 3) or the PL excitationoptical beam (308 of FIG. 3), when the environment electric field ispresent. The decay dynamics for the PL emission is shown by the curve406. The curve may be fit by the processor 120 of FIG. 1 to, forexample, a stretch exponential decay (see below) or other physicalmodel. A first set of fitting parameters from this fitting may berecorded. Further, the difference between curve 406 and a correspondingreference curve measured by the sensor 102 without the presence of theenvironmental electric field may be obtained by the processor 120 ofFIG. 1. Such corresponding reference curve may be pre-measured andrecorded in the database 122 of FIG. 1. The difference curve 416 intransient PL 414 is shown in FIG. 4b as a function of time 412. Thedifference curve 416 may be further processed by the processor 120 intoa second set of fitting parameters (see below). Characteristics of theenvironmental electric field may be determined based on the second setof fitting parameters and/or the first set of fitting parameters.

In an alternative optical configuration, the first optical beam 109, thesecond optical beam 111 and the PL excitation optical beam 115 maybeconfigured as CW optical beams and the measurement of PL emission fromthe sensor 102 may be made under steady-state. Again, the steady-statePL emission under the influence of the environmental electric field maybe compared with a pre-measured reference steady state PL emissionwithout the environmental electric field and pre-stored in the database122 of FIG. 1. The difference between the steady state PL emission withand without the environmental electric field may be used by theprocessor to determine the characteristics of the environmental electricfield.

FIG. 5 shows another optical configuration 500 as a function of time t(522) that may be used for determining characteristics of theenvironmental electric field in conjunction with the systemconfiguration of FIG. 1. In particular, the first optical beam 109 forpreparing the sensor 102 into the optically bright first charge statemay be configured into a first optical pulse 502. The second opticalbeam 111 for inducing charge conversion (between the optically brightfirst charge state and the optically dark second charge state) and forinducing the PL emission from the optically bright first charge statemay be configured as a sequence of optical pulses, e.g., 512, 514, 516,and 518 following the first optical pulse 502 by a delay of Δ₃. Theoptical pulses 512-518 may be arranged with a pulse periodicity T 510,corresponding to a pulse frequency F=1/T. The pulse frequency F may betunable. The optical pulses 512-518 with tunable pulse frequency F maybe generated directly from the second optical source 106. Alternatively,these pulses may be generated using optical components external to thesecond optical source 106 to modulate the optical beams output from thesecond optical source 106. The PL characteristics, such as the peak PLintensity of the transient PL emission, or differential PL of the PLemission with a reference PL emission from the sensor 102 (denoted asAPL) may be monitored as a function of the pulse frequency F.

An example of such measurements 600 is shown in FIG. 6 with the presenceof an environmental electric field (showing PL or ΔPL 603 as a functionof pulse frequency 601). In FIG. 6, the exemplary environmental electricfield comprises a radio-wave or microwave frequency electromagnetic wavewith frequency ƒ. FIG. 6 shows dip 602 in the measured PL intensity orΔPL as the pulse frequency F for the first and second optical beams istuned or swept. The dip 602 appears at a pulse frequency F=ƒ, 610,corresponding to the frequency of the environmental radio-wave ormicrowave frequency electric field. Other dips, such as dip 604 and 606may also be measured at subharmonic frequencies of ƒ, e.g., at ƒ/2 (612)and ƒ/3 (614). As such, the implementation of FIGS. 5 and 6 provide amanner in which the frequency of the environmental radio-wave ormicrowave frequency electric field may be determined, in addition to itsmagnitude as described above.

FIG. 7 shows a logic flow 700 for an exemplary implementation ofdetermining one or more characteristics of an environmental electricfield using the system configuration of FIG. 1. In logic block 702, anelectrometry sensor is disposed or present in an environment having anenvironmental electric field. The electrometry sensor may comprise asemiconductor lattices having at least one vacancy. In logic block 704,the sensor is optically prepared into an optically bright (or dark)charge state associated with the vacancy. In logic block 706, chargeconversion between the optically bright (or dark) charge stateassociated with the vacancy and an optically dark (or bright) chargestate associated with the vacancy is induced optically. In logic block708, photoluminescence is induced from the optically bright charge stateand at least one characteristics of the photoluminescence is monitored.In logic bock 710, the measured characteristics of the photoluminescenceemitted from the sensor is compared with a corresponding pre-measuredreference characteristics of a reference photoluminescence emitted bythe sensor. The reference characteristics of the referencephotoluminescence may be pre-measured following logic blocks 704, 706,and 708, but without the presence of the environmental electric field.The pre-measured reference characteristics of the referencephotoluminescence may be stored in a database. In one implementation forthe logic block 710, a difference between the measured characteristicsof the photoluminescence and the reference characteristics of thereference photoluminescence may be obtained. In logic block 712, the oneor more characteristics of the environmental electric field aredetermined according to the difference obtained in the logic block 710.

FIG. 8 shows a logic flow 800 for an exemplary implementation ofdetermining a characteristics of an environmental radio-wave ormicrowave frequency electric field using the system configuration ofFIG. 1. In logic block 802, an electrometry sensor is disposed in anenvironment having the environmental radio-wave or microwave frequencyelectric field. The electrometry sensor may comprise a semiconductorlattice having at least one vacancy. In logic block 804, the sensor isoptically prepared into an optically bright charge state associated withthe vacancy using a first sequence of optical pulses having a pulseperiodicity of T. In logic block 806, charge conversion between theoptically bright charge state associated with the vacancy and anoptically dark charge state associated with the vacancy is inducedoptically using a second sequence of optical pulses having the pulseperiodicity of T. In logic block 808, photoluminescence is induced fromthe optically bright charge state and the characteristics of thephotoluminescence is measured while tuning or sweeping F=1/T. In block810, a characteristics of the environmental radio-wave or microwavefrequency electric field, such as its frequency, is determined based onthe measured characteristics of the photoluminescence at various F.

In the implementations above, the charge conversion is optical inducedor controlled between optically bright state and optically dark state.Such charge conversion may be affected by the presence of theenvironmental electric field. As a result, the environmental electricfield may then modify the photoluminescence from optically bright state.Such effect on photoluminescence may be monitored to determine theamplitude, frequency, or other characteristics of the environmentalelectric field. In some other implementations, conversion may beoptically induced between two optically bright states. Such conversionmay similarly be affected by the presence of the environmental electricfield. The two optically bright states may produce photoluminescence ofdifferent characteristics (for example, in intensity and/or wavelength).By monitoring the characteristics of the photoluminescence from one orboth of the two optically bright states, the characteristics of theenvironmental electric field may be determined based on similarunderlying principles discussed above.

The electrometry sensor above is based on the effect of an electricfield being sensed on the charge conversion between optically brightstate and dark state in the sensor, and such effect is detected bymonitoring photoluminescence emission from the optically bright chargestate. In some implementations, the effect of the electric field on thephotoluminescence may be non-linear as a function of the amplitude ofthe electric field, particularly when the electric field is small. Forexample, differential photoluminescence (with and without the electricfield) in some electrometer sensors described above may dependquadratically on the amplitude of the electric field. As such, thedetection configuration of FIG. 1 may not provide an electrometry sensorhaving a linear response as a function of the amplitude of the electricfield being sensed.

In some implementations alternative to FIG. 1, the electrometry sensorand the detection configuration may be modified to provide a desiredlinear response. An exemplary modified detection configuration fordetecting electric field E_(sensed) (101) at a frequency ƒ_(sensed) isshown in FIG. 9. The detection configuration of FIG. 9 is similar toFIG. 1, except that (1) an additional reference electric field E_(ref)(904) at frequency ƒ_(ref) from source 902 is applied to theelectrometry sensor 102 such that the electrometry sensor is exposed toboth the electric field being sensed, E_(sensed) (101), and thereference electric field 904, (2) a lock-in amplifier 908 is used foranalyzing the photoluminescence 117 detected by the optical detector118, (3) signal 911 detected from the lock-in amplifier 908 may befurther processed by computer processor 120, (3) an auxiliary signal 906indicating the frequency ƒ_(ref) of the reference electric field E_(ref)(904) may be provided to the processor 120, and (4) in comeimplementations (coherent heterodyne detection described below), asecond auxiliary signal 907 indicating the phase of the referenceelectric field E_(ref) (904) may be provided to the lock-in amplifier.As will be shown in more detail below, the addition of the referenceelectric field E_(ref) (904) to the electrometry sensor may provide thedesired detection linearity by implementing a heterodyne detectionconfiguration.

For example, the differential photoluminescence 117 detected by theoptical detector 118 may be quadratic to the amplitude of the totalelectric field present in the sensor, including both the electric fieldbeing sensed E_(sensed) (101) and the reference electric field E_(ref)(904):

ΔPL∝E _(sensed) exp(i2πƒ_(sensed) t)+E _(ref) exp(i2πƒ_(ref) t+)|² =|E_(sensed)|2+|E _(ref)|²+2E _(sensed) E _(ref) cos(2πΔƒt+ϕ).  (1)

where Δƒ denotes the difference or beat frequency between ƒ_(sensed) andƒ_(ref), t represents time, and ϕ represents the phase differencebetween the electric field E_(sensed) (101) and the reference electricfield E_(ref) (904).

The differential photoluminescence thus may include a component at thebeat frequency Δƒ, with an amplitude being the inner product of theamplitudes of the electric field E_(sensed) (101) and reference electricfield E_(ref) (904). The lock-in amplifier 908 may then be used as anarrow band filter to isolate this photoluminescence component at thebeat frequency Δƒ and this photoluminescence component would be a linearfunction of the amplitude of the electric field being sensed E_(sensed)(101). The filter bandwidth of the lock-in amplifier corresponds to anintegration time constant of the lock-in amplifier. The integration timeconstant may be adjusted to any values. For example, the integrationtime constant may be 1 ms to 10 seconds. For a particular example, theintegration time constant may be 50 ms, corresponding to a FWHMfiltering bandwidth of ˜6.5 Hz. Using the lock-in amplifier 908 as anarrow band filter is merely one example. Other alternatives may beused. For example, the photoluminescence signal from the opticaldetector 118 may be input into an analog to digital converter and theconverted digital signal may be processed using a computer-implementednumerical filter having a desired filtering bandwidth.

Some implementations for the electrometry sensor 102 of FIG. 9, as shownin more detail in FIG. 10a , may include integrated electrodes forapplying the reference electric field E_(ref) (904). As such, theelectrometry sensor 102 may include lattice host 1008 with defect statessupporting charge conversion (such as the material system shown in FIG.2) and integrated pair of electrodes 1002 and 1004 for applying thereference electric fields 904. For example, electrode 1002 may beconnected to ground whereas electrode 1004 may be connected to source902. In some alternative implementations, a 180-degree hybrid splittermay be used to alternate positive and negative potential at electrodes1002 and 1004 rather than having one of the electrodes always at ground.The electrodes 1002 and 1004 may be integrated with the lattice host1008 using current and future technologies for growing, depositing, andpatterning electrodes. During operation of the electrometry sensor 102,the electric field being sensed (not shown in FIG. 10a ) would be inco-existence with the reference electric field E_(ref) (904). Asdescribed above, the electrometry sensor 102 may be optically prepared,charge-transferred, and optically excited using optical excitation 1012.Photoluminescence 1013 may be detected by optical detector 1016, whichis then sent to the lock-in amplifier as depicted in FIG. 9.

The in-plane direction of the reference electric field E_(ref) (904) maybe determined by the in-plane positions of the electrodes, as shown inan in-plane view of the electrodes in FIG. 10b . FIG. 10b shows that apair of electrodes 1022 and 1024 may be used to apply a referenceelectric field in the orientation shown by 1030, whereas a pair ofelectrodes 1026 and 1028 may be used to apply a reference electric fieldin the orientation shown by 1032. As shown by Equation (1) above, thephotoluminescence at the beat frequency Δƒ is non-zero when the electricfield E_(sensed) being sensed and the reference electric field E_(ref)are not normal to each other and would be at maximum when E_(sensed) andE_(ref) are aligned along the same orientation. In other words, theelectric fields in Equation (1) may be considered as vectors and theinner product of the electric fields E_(sensed) and E_(ref) is non-zeroonly when the electric fields are not orthogonal to each other. As such,for maximum detection signal for the photoluminescence component at thebeat frequency, multiple electrode pairs may be integrated into theelectrometry sensor such that the electrometry sensor may be capable ofapplying reference electric field in various in-plane orientations. Forexample, the electrodes may be arranged and segmented in a circularfashion around the detection region of the electrometry sensorsurrounded by the electrodes. In some other implementations, theelectrodes may be disposed on the back side of the sensor, particularlywhen the sensor is sufficiently thin. Such electrode configuration maybe used to apply out-of-plane reference field. When the electrometrysensor is in operation, a pair of electrodes may be chosen (depending onthe orientation of E_(sensed)) to obtain maximum photoluminescencecomponent at the beat frequency. In some other implementations, theconfiguration of the electrodes may not be limited to in-planeconfiguration. For example, the electrode pairs may be arranged in threespatial dimensions. As such, an electrode pair may be chosen forapplying the reference electric field that is aligned with the electricfield being sensed in any orientation in three-dimensional space. Insome other implantations of the electrometry sensor, the electrodes maybe configured as shown in the in-plain configuration of FIG. 10b , or ina configuration where a single pair of electrodes are used, and suchelectrometry sensor may be mounted on, e.g., a piezo-electric platformthat may be used to orient the electrometry sensor such that thereference electric filed is aligned to the electric field being sensedfor obtaining maximum photoluminescence component at the beat frequency.

When the electrometry sensor of FIG. 9 is in operation, the lock-inamplifier detects signal from the optical detector 118 centered at alock-in frequency equal to Δƒ (or ƒ_(lock-in)−Δƒ=0), and the signaltails off on either frequency side according to the filtering bandwidth(or integration time constant) of the lock-in amplifier, as shown inFIG. 11. In one implementation, the lock-in amplifier may be set at afixed detection frequency f_(lock-in) and measurements may be made asthe frequency ƒ_(ref) of the reference electric field E_(ref) is tunedto obtaining the curve 1106 in FIG. 11. The signal reaches maximum 1107when Δƒ ƒ_(ref)−ƒ_(sensed) equals ƒ_(lock-in), as shown by 1102 and1104, and falls off beyond the filtering bandwidth of the lock-inamplifier on either frequency side of the maximum 1107, as shown by theFWHM 1108. For example, ƒ_(lock-in) may be fixed at 397 Hz, theintegration time constant for the lock-in amplifier may be adjusted to50 ms (corresponding to a FWHM filtering bandwidth of 6.5 Hz), and theƒ_(sensed) may be 68 MHz. When the ƒ_(ref) is tuned, the lock-inamplifier may detect maximum signal at an ƒ_(ref) of 68 MHz+397 Hz (or68 MHz-397 Hz), with a FWHM of about 6.5 Hz.

In another alternative implementation, frequency ƒ_(ref) of thereference electric field may be fixed while the lock-in detectionfrequency ƒ_(lock-in) is tuned. Similar curve 1108 may be obtained withmaximum signal when ƒ_(lock-in) is tuned to a frequency such thatƒ_(lock-in)−Δƒ=0.

In any of the implementations above according to FIG. 11, the detectedsignal level from the lock-in amplifier is linear to the amplitude ofthe electric field E_(sensed) being sensed. The total photoluminescencedetected by the photodetector 118 of FIG. 9 includes not only thedifferential photoluminescence (with and without electric field) butalso the background photoluminescence generated by the input opticalexcitation without the electric fields. However, such backgroundphotoluminescence would not be at the beat frequency Δƒ and would atmost contribute as some noise to the signal detected by the lock-inamplifier 908. Such noise may be minimized by increasing the integrationtime constant (or reducing the filtering bandwidth) of the lock-inamplifier.

As such, the amplitude of E_(sensed) can be sensed with linearity. Inaddition, the frequency ƒ_(sensed) can be determined as shown in FIG. 11by tuning ƒ_(lock-in) or ƒ_(ref). The measured signal is also linearwith the amplitude of the applied reference electric field, therebyproviding another convenient tuning knob for the measurement. Forexample, tuning of the characteristics of the reference electric fieldmay enables tuning of a dynamic range of the sensor, i.e. the optimalrange of electric field that can be detected (see description below withrespect to FIG. 17b ). Further, as shown in FIG. 10b and describedabove, the orientation of E_(sensed) may be determined, by amulti-electrode configuration or by scanning the orientation of theelectrometry sensor in time. In some implementations, multiple pairs ofelectrodes of FIG. 10b may be used to apply reference electric fields ofdifferent frequencies. In such a manner, different orientations would beassociated with corresponding different beat frequencies for measuringelectric field along each of the orientations simultaneously.

In the above description associated with FIGS. 9-11, Equation (1) hasbeen assumed. In other words, it has been assumed that the differentialphotoluminescence is quadratic to the amplitude of the electric fields.However, the implementations above may also be applicable to other typeof nonlinear photoluminescence response (e.g., cubic, or a mixture ofquadratic and cubic, etc.). The lock-in amplifier would isolate thephotoluminescence signal component at the beat frequency between theelectric field being sensed E_(sensed) and the reference electric fieldE_(ref). Such photoluminescence signal component would be linear withrespect to E_(sensed).

In some other implementations, the heterodyne detection above may befurther modified to utilize a coherent heterodyne detection, where, inaddition to the frequency relation, there may be also a known phaserelation between the reference electric field and electric field beingsensed (phase ϕ in Equation (1)). In particular, if this ϕ is notrandom, that is, the phase of the electric field being sensed can beknown (for example if the electric field being sensed can be driven ortriggered), then the sensitivity of the detection will be even higher.It allows more efficient averaging of the signal than for random phase.The phase also corresponds to the relative direction (sign) in additionto just orientation between sensed and reference electric field. Withoutthis known phase, it is possible to know the orientation but not thesign of the vectors in space for the electric field. Coherent heterodynecould therefore allow real 3D vector imaging with high sensitivity.

FIG. 12 illustrates an exemplary logic flow 1200 for the implementationsof FIGS. 9-11. In step 1201, the electrometry sensor is disposed in anenvironment having an electric field to be sensed. In step 1202, areference electric field is applied to the environment via, for example,the electrometry sensor, in addition to the electric field being sensed.In step 1204, the electrometry sensor is optically prepared into anoptically bright charge state. In step 1206, charge conversion isinduced from the optically bright (or dark) charge state to theoptically dark (or bright) charge state in the electrometry sensor inthe presence of both the electric field being sensed and the referenceelectric field. In step 1208, photoluminescence from the opticallybright charge state in the electrometry sensor is induced and monitoredby an optical detector. The signal detected by the optical detector isfurther processed by a narrow band filter such as a lock-in amplifier.In step 1210, the signal derived from the narrow band filter is furtherprocessed to obtain various characteristics of the electric field beingsensed as described above in with respect to FIGS. 9-12.

More details, including various characterization, measurements, andapplication of the electrometry system above in exemplary materialsystems are described below.

Charge state of defects in semiconductor may be optically detected usingthe methods and systems described herein. For example, fornitrogen-vacancy (NV) center in diamond, a change from the NV⁻ to theNV⁰ provides different emission spectra, while in VV or siliconvacancies (V_(Si)) in 4H and 6H—SiC, only one charge state (VV₀, V_(Si)⁻) has a PL spectrum. Charge conversion between the various chargestates can be efficiently realized by optical pumping at specificwavelengths. This change in PL due to optical charge conversion (OCC)rate between the bright and dark charge states of both VV and V_(Si)defects may be modulated by the presence of an applied radio-wavefrequency (RF) or microwave (MHz to GHz) electric field, which cantherefore be measured by photoluminescence. The frequency range of thiselectrometry by OCC, or electrometry by OCC (EOCC), would be extremelychallenging using spin sensing. In general, a defect may have two chargestates (which can both be optically bright, as an alternative to theoptically bright and dark charge state combination shown as an exampleabove) associated with different PL; a change in PL due to opticalcharge conversion (OCC) rate between the two charge states of the defectmay be modulated by the presence of an applied radio-wave frequency (RF)or microwave (MHz to GHz) electric field, which can therefore bemeasured by photoluminescence.

In an exemplary host material of 4H—SiC, OCC of divacancy ensembles maybe realized using a near or above bandgap (3.2 eV) excitation toefficiently obtain VV⁰ (bright), while an illumination below 1.3 eVpumps the defect toward a dark charge state, either VV⁻ or VV⁺. Forexample, 365 nm (continuous) or 405 nm (pulsed) optical excitation froma laser may be used for excitation of the detects into the bright chargestate and 976 nm optical excitation from a laser may be used for OCCfrom the bright charge state to the dark charge state. The 976 nm laseralso exciting PL from VV⁰. A schematic of the setup is shown in FIG. 13a, where the two laser beams are focused at a divacancy layer (carbonimplantation) between two metal contacts on top of the SiC substrate.

In one exemplary implementation, to characterize and detect OCCtransient decays due to the 976 nm pumping immediately following resetby 405 nm, a fast photo detector is used to capture a complete transientfrom bright to dark in a single measurement, as shown in the top panelof FIG. 13b . The decay may be fitted by a simple stretch exponentialdecay f(t)∝exp(−(Rt)^(n)), where R is the characteristic decay time andn the stretch factor, the latter describing the complexity of the chargeconversion mechanism (n=1 for simple photoionization and n<1 forcompetition between ionization, carrier capture and carrier diffusion).An RF electric field E (root mean square amplitude, frequency ƒ_(E)=10MHz) is then applied during the 976 nm illumination. The PL difference(ΔPL) with electric field minus is plotted in the bottom panel of FIG.13 b.

The transients may be fitted by shifts, for example in the conversionrate R and with n being fairly constant (˜1% shift). Shifts in R areshown as a function of E in FIG. 13c and may follow a quadraticdependence with saturation such that

ΔR(E)=ΔR _(∝)<(E/E _(sat))²/(1+(E/E _(sat))²)>_(t)  (2)

where < >_(t) correspond to a time average over an oscillation of the RFelectric field, ΔR_(∝) is the maximum R shift when E>>E_(sat). In thisexemplary implementation, ΔR_(∝)=27±1% and E_(sat)=158±20 V/cm. Thesevalues may be specific to the sample or to the defect itself. EOCC wouldbe likely due to variations in carrier recapture after ionization andwould depend on parameters such as electron mobility or drift velocity.E_(sat) may be directly related to the defect potential and changes inphotoionization and capture cross-sections.

From the quadratic response given by Equation (2), the sensitivity ofthis sensing technique to electric field can be defined as:

S=(E ²σ_(ΔPL)(E)(T _(exp))^(1/2))/(ΔPL(E))  (3)

where ΔPL/σ_(ΔPL) is the signal-to noise ratio (using standarddeviation) for a given electric field (below saturation) and T_(exp) isthe experiment time. In FIG. 13d , this sensitivity is measured as afunction of the 976 nm pump power. For better sensitivity, themeasurement is realized with continuous 976 nm and 365 nm (replacing the405 nm) illumination while locking-in on the electric field turnedperiodically on and off. For this particular implementation, sensitivityat 10 MHz is measured as low as 41±8 (V/cm)² Hz^(−1/2) for an estimatedensemble of 10⁴ VVs within the confocal spot size.

The frequency response of the EOCC technique is shown in FIG. 14a wherethe rate shift from transient experiments are fitted and plotted as afunction of frequency, from low frequency AC (100 Hz) to microwavefrequencies (2 GHz). Above 1 GHz, the rate shift from electric fielddecreases from parasitic capacitances (RC filtering). Below 1 MHz, adecrease in rate shift is also observed and may be attributed to thecreation of a space charge under illumination and electric field. At lowfrequency, when defects are ionized the resulting carriers aredistributed such that they compensate the local electric field. At highenough frequency, the distribution never reaches its steady state andthe space charge is not created. The characteristic timescale for spacecharge formation is the Maxwell relaxation time (1/f_(M))=ε₀ε_(r)ρ/2,where ε₀ and ε_(r) (≈10 for 4H—SiC) are the vacuum and relativepermittivity and ρ is the resistivity. Within this description and usinga fitting function for ƒ_(M), the resistivity may be estimated to be≈10⁷ Ωcm. The space charge creation may be dependent on the initialcharge distribution which may be modified by increasing the spot size.

In a further implementation, frequency and phase of the applied RFelectric field may be sensed and resolved as shown in FIGS. 14b and 14c. This is enabled by pulsing the 976 nm pump light with a givenfrequency ƒ_(laser) and duty cycle. First, ƒ_(laser) is fixed whileƒ_(E) is swept with a random initial phase between the two frequencies.This sequence provides a measure of the effective filter function of thepulse sequence, showing dips of decreasing intensities for ƒ_(E) equalto increasingly higher harmonics of ƒ_(laser) (FIG. 14b ). The dips maybe explained by the fact that, even with random phase, the light pulsealways encounters the same value of the electric field when ƒ_(E)matches a harmonic of ƒ_(laser). The RF electric field effectivelybecomes DC and the EOCC signal diminishes as expected from FIG. 14a .The effect is increasingly prominent for decreasing duty cycle and thefilter function sharpens. For phase resolution (FIG. 14c ), the laserpulse and electric field oscillations have a fixed phase relative to oneanother, and ƒ_(laser)=2ƒ_(E). Alternating light pulses encounterelectric fields with alternating signs but equal amplitude depending onthe phase. Hence, the electric field (E²) oscillation in time can bedirectly mapped by sweeping the relative phase with the pulsed laser.The model in the figure may be directly calculated without any freeparameter using Equation (2) and the overlap between the electric fieldwave and the laser pulse.

While the discussion above focuses on EOCC characterization forensembles of VV in 4H—SiC, the underlying implementations and techniquesmay be generalizable to other defects. For example, silicon vacancyV_(Si) in 4H—SiC, may be optically active up to room temperature. Thecombination of a 365 nm (pump to the dark state) and a 785 nm (pump tothe bright state) excitation may be used for charge conversion, and maytherefore be used for EOCC as shown in FIGS. 15a and 15b . The change inPL (continuous illumination) as a function of electric field is plottedin FIG. 15a as a function of electric field for temperatures from 5 K to350 K. The data may fitted by the processor 120 according to Equation(2), and the PL change for E→∞ is plotted as a function of temperaturesin FIG. 15b . The EOCC signal may be measured at all temperatures with adrastic reduction above 30-77 K. This behavior may be explained by thethermal activation of shallow impurities or capture barriers forexample.

In another implementation, EOCC discussed above may be applied to mapsurface acoustic wave (SAW) modes in an electro-mechanical resonator in4H—SiC. The mapping may be implemented by detecting the electric fieldand piezoelectrically induced by a strain field using the electrometrymethod above. An example of the resonator is shown in FIG. 16a with aninterdigital transducer (IDT) fabricated on top of a 500 nm AlN layer ontop of the SiC substrate. The resonator is composed of Bragg gratingsmade from grooves in the AlN that act as reflective mirrors, while theIDT couples the electrical drive to the SAW mode. FIGS. 16b, 16c and 16drespectively show a longitudinal (x-z) cross-section in the center of adevice where there is a window in the IDT, a cut (x) across the AlNgrooves and a transverse cut (y) in the central window. In thecross-section, wave crests separated by half of the wavelength λ (λ=16μm, cavity frequency is 421 MHz) may be observed within the window, dueto, for example, a quadratic response in electric field. In FIG. 16c ,the cut through the grooves shows oscillations from the SAW modulated byan exponential decay. In this particular implementation, thecharacteristic decay length into the Bragg grating is measured to beL=0.78±0.03 mm, and directly related to the reflectivity per gratingstrip |r_(s)|=λ/4L=0.51±0.02%.

In FIG. 16d , a transverse cut is shown as a function of drive frequencyof the cavity, allowing for observation of the transverse modes of thisimplementation of the SAW resonator. Modes with 1 to 5 peaks areobserved. Their total signal may be separately integrated, plotted inthe bottom panel of FIG. 12d , and compared with a direct RF reflection(S₁₁) measurement of the cavity. The S₁₁ signal shows the totalcontribution from all modes, whereas the EOCC implementation is able tofully separate these contributions. EOCC may therefore providecomplementary information (to displacement) to common MEMScharacterization methods such as laser Doppler vibrometry and varioussurface techniques (scanning electron microscope, atomic forcemicroscopy, etc.).

FIG. 17a shows a typical nonlinear relationship 1702 between themeasured EOCC and the amplitude of the electric field being sensed usingthe detection implementations of FIGS. 1-8 (standard detection).However, by using the heterodyne detection implementations of FIGS.9-12, the measured and filtered EOCC becomes linear as a function of theamplitude of the electric field being sensed above the noise floor, asshown in FIG. 17b . In particular, FIG. 17b shows the relationshipbetween the EOCC in log scale and power of the electric field in dBm asa linear relationship with a slope of 1/20, which corresponds to linearrelationship between EOCC in linear scale and amplitude of the electricfield in linear scale. FIG. 17b further shows heterodyne EOCCmeasurements under different amplitudes for the reference electricfield, as indicated by 1704 (18 dBm), 1706 (13 dBm), and 1708 (8 dBm).FIG. 17b shows that at higher reference electric field, such as in 1704,in comparison to lower reference electric field, such as 1708, loweramplitudes for the electric filed being sensed can be measured in thepresence of noise, providing larger or shifted measurement dynamicrange, as shown by region 1710 of FIG. 17 b.

FIGS. 18a and 18b show heterodyne detection measurements for anelectrometry sensor having a reference electric field applied in thehorizontal orientation parallel to an electric field being sensed and inthe vertical orientation orthogonal to the electric field being sensed,respectively. FIGS. 18a and 18b indicate that a photoluminescencecomponent at the beat frequency between the reference electric field andthe electric field being sensed can be measured (1802) when the twofield are parallel, and that such photoluminescence component is absent(1804) when the two electric fields are orthogonal, consistent with thedescription above with respect to FIG. 10.

FIGS. 19a-19d shows exemplary coherent heterodyne measurements, in whichthe sign (direction) of the electric filed in the vector space (not justorientation without sign information) may be determined. FIGS. 19a and19b are similar to FIGS. 18a and 18b . The coherent measurement howeverprovides both magnitude and phase of the detection. The magnitude is thesame in both coherent and incoherent detection, but only coherentmeasurement can give the phase relationship (between the electric fieldbeing sensed and the reference electric field), which may be obtainedfrom the lock-in). Correspondingly, FIGS. 19c and 19d plots the phasemeasurements from the lock-in amplifier. As shown by FIG. 19c , when twoelectric fields are aligned (in orientation, i.e., the same sign anddirection), the phase is always 0. When the two electric fields areorthogonal to one another (by, for example, applying the two electricfields using electrodes that orthogonal), the electric fields arealigned (of the same sign) in 2 out for 4 space quadrants and oppositesign (phase 180 degrees) in the other 2 of the 4 space quadrants, asshown in FIG. 19d . The electric fields are indicated by the arrows inFIG. 19 d.

As such, the electrometry implementations disclosed above and based onelectric field dependent charge state conversion in semiconductors maybe used to detect various characteristics of an environmental electricfield, in a wide spectral range (e.g., radio wave and microwavefrequencies). Such electrometry systems may be used to detect thepresence of environmental electrical field in a binary manner. Inaddition, various characteristics of the environmental electric filedmay be detected (e.g., magnitude and spectral frequency).

While the particular invention has been described with reference toillustrative embodiments, this description is not meant to be limiting.Various modifications of the illustrative embodiments and additionalembodiments of the invention, will be apparent to one of ordinary skillin the art from this description. Those skilled in the art will readilyrecognize that these and various other modifications can be made to theexemplary embodiments, illustrated and described herein, withoutdeparting from the spirit and scope of the present invention. It istherefore contemplated that the appended claims will cover any suchmodifications and alternate embodiments. Certain proportions within theillustrations may be exaggerated, while other proportions may beminimized. Accordingly, the disclosure and the figures are to beregarded as illustrative rather than restrictive.

1. A method for sensing an electric field in an environment, comprising:pre-exciting a sensor comprising a crystalline lattice and at least onedefect in the crystalline lattice to prepare the at least one defect ina first charge state using a first optical beam at a first opticalwavelength; converting the at least one detect from the first chargestate to a second charge state, using a second optical beam at a secondoptical wavelength, photoluminescence associated with the first chargestate being different from the second charge state; monitoring one ormore characteristics of a photoluminescence emitted during or after theconversion of the at least one defect from the first charge state to thesecond charge state; and determining one or more characteristics of theelectric field in the environment according to the one or more monitoredcharacteristics of the photoluminescence.
 2. The method of claim 1,further comprising pre-determining one or more reference characteristicsof a reference photoluminescence emitted by the sensor without beingdisposed in the environment and excited by the first optical beam andthe second optical beam, wherein determining the one or morecharacteristics of the electrical field in the environment according tothe monitored one or more characteristics of the photoluminescencecomprises: determining a difference between the one or more monitoredcharacteristics of the photoluminescence and the one or morecharacteristics of the reference photoluminescence; and determining theone or more characteristics of the electrical field in the environmentaccording to the difference.
 3. The method of claim 1, wherein the firstoptical beam comprising a first pulse of light at the first opticalwavelength and the second optical beam comprises a second pulse of lightat the second optical wavelength following the first pulse of light. 4.The method of claim 1, further comprising fitting the photoluminescenceto a stretch exponential decay, or other physical model, to obtaining aset of fitting parameters, wherein determining the characteristics ofthe electric field in the environment comprises determining thecharacteristics of the electric field in the environment according tothe set of fitting parameters.
 5. The method of claim 1, wherein thesecond optical beam comprises a sequence of pulses having a pulsingfrequency, the method further comprising: sweeping the pulsing frequencyfor the second optical beam while monitoring the characteristics of thephotoluminescence; and determining an oscillation frequency of theelectric field in the environment.
 6. The method of claim 5, wherein theone or more characteristics of the electric field in the environmentcomprise an electric field amplitude, and wherein determining the one ormore characteristics of the electric field in the environment accordingto the one or more monitored characteristics of the photoluminescencecomprises: obtaining one or more reference characteristics of areference photoluminescence emitted by the sensor when disposed in areference electric field having the oscillation frequency; anddetermining the electric field amplitude of the electric field in theenvironment according to the one or more characteristics of thephotoluminescence and the one or more reference characteristics of thereference photoluminescence.
 7. The method of claim 1, wherein thecrystalline lattice comprises a silicon carbide lattice comprising a4H—SiC or a 6H—SiC crystalline lattice.
 8. (canceled)
 9. (canceled) 10.The method of claim 7, wherein at least one defect comprises at leastone silicon vacancy or divacancy.
 11. (canceled)
 12. (canceled) 13.(canceled)
 14. (canceled)
 15. The method of claim 1, wherein the firstoptical wavelength is shorter than the second optical wavelength. 16.The method of claim 15, wherein the first optical wavelength is in awavelength range of 340 and 430 nanometers and the second opticalwavelength is in a wavelength range of 700 and 1100 nanometers. 17.(canceled)
 18. The method of claim 1, wherein the one or morecharacteristics of the photoluminescence is monitored at a third opticalwavelength and wherein the second optical wavelength is shorter than thethird optical wavelength.
 19. The method of claim 1 wherein the firstoptical beam comprises a pulse and the second optical beam comprises acontinuous wave optical beam.
 20. The method of claim 1, furthercomprising: disposing the sensor in an electro-mechanical device whereinthe electric field in the environment comprises piezoelectric fieldgenerated by the electro-mechanical device; and mapping surface acousticmodes of the electro-mechanical device using the monitored one or morecharacteristics of the electric field in the environment.
 21. The methodof claim 1, wherein the electric field is piezoelectrically induced froma strain field or stress field in the crystalline lattice, the methodfurther comprising determining one or more characteristics of the strainfield or the stress field and one or more characteristics of a strain ora stress in the crystalline lattice producing the electric fieldaccording to the one or more monitored characteristics of thephotoluminescence.
 22. The method of claim 1, further comprisingapplying a reference electric field to the environment beforepre-exciting the sensor, wherein the one or more monitoredcharacteristics of the photoluminescence correspond to aphotoluminescence component at a beat frequency between the electricfield being sensed and the reference electric field.
 23. The method ofclaim 22, wherein the photoluminescence component at the beat frequencyis extracted using a narrow band filter.
 24. The method of claim 15,wherein the photoluminescence component is measured based on aheterodyne detection.
 25. The method of claim 1, wherein the firstcharge state is one of an optically bright and dark charge state, andthe second charge state is the other of the optically bright and darkcharge state.
 26. A system comprising: a sensor comprising a crystallinelattice having at least one defect; a first optical source emitting afirst optical beam at a first optical wavelength; a second opticalsource emitting a second optical beam at a second optical wavelength; anoptical detector for monitoring a photoluminescence from the sensor whenthe sensor is excited by the first optical beam and the second opticalbeam; a database; a processor configured to: extract a first set ofparameters from the photoluminescence; obtain a second set ofpredetermined parameters from a reference photoluminescence measured bythe sensor and stored in the database; obtain a difference between thefirst set of parameters and the second set of predetermined parameters;and determine an environmental electric field of the sensor according tothe difference.
 27. A system for measuring characteristics of anenvironmental electric field, comprising: a sensor comprising acrystalline lattice having at least one defect and a pair of electrodesfor applying a reference electric field; a first optical source emittinga first optical beam at a first optical wavelength; a second opticalsource emitting a second optical beam at a second optical wavelength; anoptical detector for generating a electric signal by collecting aphotoluminescence from the sensor when the sensor is excited by thefirst optical beam and the second optical beam in presence of theenvironmental electric field and the reference electric field; and acircuitry configured to: filter the first signal to obtain a signalcomponent at a beat frequency between the environmental electric fieldand the reference electric field; and extract the characteristics of theenvironmental electric field based on the signal component andcharacteristics of the reference electric field.